where the matrix \(A\)  is constructed as follows.
Let us consider the incidence matrix \(B\)  of the undirected graph \(\mathcal {G}\) . For each vertex \(v\) , \(A\)  contains a \(\frac{d_v}{2}\)  number of identical rows of \(B\) . This implies that \(A\)  is square and of size equal to the number of edges of \(\mathcal {G}\) . The formula above is exact but hard to use, given the fact that the permanent is rather hard to calculate, being \(\#P\) -complete [1]}. However, one can upper bound the permanent of \((0,1)\)  matrices using the Bregman-Minc result for the permanent [2]}, which is
\(\text{perm}(A)\le \prod _{i=1}^m (r_i!)^{\frac{1}{r_i}},\) 
